Efficient 5-Point Block Method for Oscillatory ODEs with Phase Lag and Amplification Error Control

Rubayyi T. Alqahtani, Anurag Kaur () and Theodore E. Simos ()
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Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia
Anurag Kaur: School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala 147004, Punjab, India
Theodore E. Simos: Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref 32093, Kuwait

Mathematics, 2025, vol. 13, issue 11, 1-41

Abstract: This research presents innovative modified explicit block methods with fifth-order algebraic accuracy to address initial value problems (IVPs). The derivation of the methods employs fitting coefficients that eliminate phase lag and amplification error, as well as their derivatives. A thorough stability analysis of the new approach is conducted. Comparative assessments with existing methods highlight the superior effectiveness of the proposed algorithms. Numerical tests verify that this technique significantly surpasses conventional methods for solving IVPs, particularly those exhibiting oscillatory solutions.

Keywords: numerical solution; initial value problems (IVPs); block methods; phase-fitting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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